where $t_0 \in \RR$ is a constant. In the comments it is also argued that one may alternatively use contour integration. I liked the article, but wondered whether the symmetry of the problem would perhaps admit a simpler approach.

Here I give a third method that uses Fourier transforms and convolutions. In order to avoid confusion about scaling factors, for definiteness we define the Fourier transform $\mathcal{F} : L^2(\RR) \to L^2(\RR)$ by